Mathematics

Problem

From a point

M

, three rays

ML, MN,

and

MP

are drawn so that

\angle LMN=(7y-29)^{\circ}

and

\angle NMP=(3y+19)^{\circ}

. The two angles are adjacent. (i) Determine the value of

y

if the sum of the two angles is

180^{\circ}

. (ii) Hence prove that rays

ML

and

MP

lie on the same straight line. (iii) Find the measure of

\angle LMP